Electronic and photonic properties of graphene layers and carbon nanoribbons.

Recent advances in fabrication techniques have made it possible to produce graphene, which is a two-dimensional honeycomb lattice of carbon atoms forming the basic planar structure in graphite. Graphene has stimulated considerable theoretical interest as a semi-metal, the electron effective mass of which may be described by an unusual massless Dirac fermion band structure. Several novel many-body interactions in graphene have been investigated. In recent experiments, the integral quantum Hall effect (IQHE) has been reported in graphene. The quantum Hall ferromagnetism in graphene has been investigated from a theoretical point of view. Graphene has a number of interesting properties as a result of its unusual band structure, which is linear around two inequivalent points (K and K′) in the first Brillouin zone. The single-electron quantum states near K and K′ are described by the Dirac equation, where the wave functions are pseudo-spinors because of the two-point basis of the honeycomb lattice. In the presence of a magnetic field, the graphene structure shifts both the Shubnikov–de Haas oscillations as well as the step pattern of the IQHE. Both these effects have recently been studied experimentally. The spectrum of plasmon excitations in a single graphene layer embedded in a material with an effective dielectric constant 3 in the absence of an external magnetic field (B = 0) was calculated. For two carbon layers, the nearest-neighbour tight-binding approximation yields a gapless state with parabolic bands touching at the K and K′ points, instead of conical bands. More accurate consideration gives a very small band overlap (about 1.6meV), but, at larger energies, bilayer graphene can be treated as a gapless semiconductor. Consequently, the QHE for bilayer graphene differs significantly from both single-layer graphene and conventional semiconductors, as found experimentally. This brief summary shows the diverse and interesting phenomena which have been studied in two-dimensional graphene as well as its related layered structural arrangements, thus making it a suitable candidate for a theme. This is an appropriate topic since research on graphene is expanding rapidly both theoretically and experimentally. There are several new developments which are discussed in this Theme Issue. These include: (i) the electron–electron and electron–hole pairing in graphene structures, (ii) Bose–Einstein condensation and superfluidity of trapped polaritons in graphene embedded in a microcavity, (iii) the electronic and optical properties of monolayer and bilayer graphene,